La4Cu3MoO12 is a cluster antiferromagnet where copper spin-1/2 trimers form a network of strongly coupled spin trimers. The magnetic properties of this material have been examined using magnetic neutron scattering. At low temperatures, excitations from the ground state are observed at 7.5(3) meV and 132.5(5) meV. An additional peak in the neutron scattering spectrum, which appears at 125.0(5) meV on heating, is ascribed to a transition between excited states. The wave vector and temperature dependence of the inelastic magnetic scattering cross section are consistent with intratrimer transitions. Magnetic neutron diffraction reveals antiferromagnetic order below TN=2.6 K with a wave vector (½00). The ordered magnetic structure is described as intertrimer order where spin correlations within trimers are controlled by the strong intratrimer interactions. Combining the information derived from elastic and inelastic magnetic neutron scattering with group theoretical analysis, a consistent set of intratrimer interactions and ordered magnetic structures is derived. The experiment provides a simple worked example of magnetism associated with interatomic composite degrees of freedom in the extreme quantum limit.